Control.Category.Discrete

Documentation

data Discrete a b where

The discrete category is the category with the minimum possible amount of arrows: for any given type, there is id, and that's all. You can use this to provide a proof that some endomorphism (of not closer specified category) is the identity.

Constructors

Refl :: Discrete a a

Instances

Category (Discrete :: k -> k -> Type)

Defined in Control.Category.Discrete

Methods

id :: forall (a :: k0). Discrete a a

(.) :: forall (b :: k0) (c :: k0) (a :: k0). Discrete b c -> Discrete a b -> Discrete a c

Category (Discrete :: κ -> κ -> Type)

Defined in Control.Category.Constrained

Associated Types

type Object Discrete o

Methods

id :: forall (a :: κ0). Object Discrete a => Discrete a a

(.) :: forall (a :: κ0) (b :: κ0) (c :: κ0). (Object Discrete a, Object Discrete b, Object Discrete c) => Discrete b c -> Discrete a b -> Discrete a c

Functor [] (Discrete :: Type -> Type -> Type) (Discrete :: Type -> Type -> Type)

Defined in Control.Functor.Constrained

Methods

fmap :: (Object Discrete a, Object Discrete [a], Object Discrete b, Object Discrete [b]) => Discrete a b -> Discrete [a] [b]

Functor Maybe (Discrete :: Type -> Type -> Type) (Discrete :: Type -> Type -> Type)

Defined in Control.Functor.Constrained

Methods

fmap :: (Object Discrete a, Object Discrete (Maybe a), Object Discrete b, Object Discrete (Maybe b)) => Discrete a b -> Discrete (Maybe a) (Maybe b)

Functor IO (Discrete :: Type -> Type -> Type) (Discrete :: Type -> Type -> Type)

Defined in Control.Functor.Constrained

Methods

fmap :: (Object Discrete a, Object Discrete (IO a), Object Discrete b, Object Discrete (IO b)) => Discrete a b -> Discrete (IO a) (IO b)

Functor Complex (Discrete :: Type -> Type -> Type) (Discrete :: Type -> Type -> Type)

Defined in Control.Functor.Constrained

Methods

fmap :: (Object Discrete a, Object Discrete (Complex a), Object Discrete b, Object Discrete (Complex b)) => Discrete a b -> Discrete (Complex a) (Complex b)

HasAgent (Discrete :: Type -> Type -> Type)

Defined in Control.Category.Constrained

Associated Types

type AgentVal Discrete a v

Methods

alg :: (Object Discrete a, Object Discrete b) => (forall q. Object Discrete q => AgentVal Discrete q a -> AgentVal Discrete q b) -> Discrete a b

($~) :: (Object Discrete a, Object Discrete b, Object Discrete c) => Discrete b c -> AgentVal Discrete a b -> AgentVal Discrete a c

EnhancedCat (Coercion :: Type -> Type -> Type) (Discrete :: Type -> Type -> Type)

Defined in Control.Arrow.Constrained

Methods

arr :: (Object Discrete b, Object Discrete c, Object Coercion b, Object Coercion c) => Discrete b c -> Coercion b c

Functor (Either a) (Discrete :: Type -> Type -> Type) (Discrete :: Type -> Type -> Type)

Defined in Control.Functor.Constrained

Methods

fmap :: (Object Discrete a0, Object Discrete (Either a a0), Object Discrete b, Object Discrete (Either a b)) => Discrete a0 b -> Discrete (Either a a0) (Either a b)

Functor ((,) a) (Discrete :: Type -> Type -> Type) (Discrete :: Type -> Type -> Type)

Defined in Control.Functor.Constrained

Methods

fmap :: (Object Discrete a0, Object Discrete (a, a0), Object Discrete b, Object Discrete (a, b)) => Discrete a0 b -> Discrete (a, a0) (a, b)

EnhancedCat (Discrete :: Type -> Type -> Type) f => EnhancedCat (Discrete :: Type -> Type -> Type) (o ⊢ f)

Defined in Control.Arrow.Constrained

Methods

arr :: (Object (o ⊢ f) b, Object (o ⊢ f) c, Object Discrete b, Object Discrete c) => (o ⊢ f) b c -> Discrete b c

EnhancedCat ((->) :: Type -> Type -> Type) (Discrete :: Type -> Type -> Type)

Defined in Control.Arrow.Constrained

Methods

arr :: (Object Discrete b, Object Discrete c, Object (->) b, Object (->) c) => Discrete b c -> b -> c

Category f => EnhancedCat (o ⊢ f) (Discrete :: Type -> Type -> Type)

Defined in Control.Arrow.Constrained

Methods

arr :: (Object Discrete b, Object Discrete c, Object (o ⊢ f) b, Object (o ⊢ f) c) => Discrete b c -> (o ⊢ f) b c

Functor ((->) a :: Type -> Type) (Discrete :: Type -> Type -> Type) (Discrete :: Type -> Type -> Type)

Defined in Control.Functor.Constrained

Methods

fmap :: (Object Discrete a0, Object Discrete (a -> a0), Object Discrete b, Object Discrete (a -> b)) => Discrete a0 b -> Discrete (a -> a0) (a -> b)

type Object (Discrete :: κ -> κ -> Type) (o :: κ)

Defined in Control.Category.Constrained

type Object (Discrete :: κ -> κ -> Type) (o :: κ) = ()

type AgentVal (Discrete :: Type -> Type -> Type) a v

Defined in Control.Category.Constrained

type AgentVal (Discrete :: Type -> Type -> Type) a v = GenericAgent (Discrete :: Type -> Type -> Type) a v